"Conservation of energy applied to a flowing fluid."
In fact, Bernoulli's equation is an application of the concepts of work and conservation of energy. For an incompressible fluid, laminar (non-turbulent) flow and no viscous acting forces (inverse fluid), the fluid energy will be constant at any point in the flow. Bernoulli's equation relates the kinetic and potential energy of the fluid to the absolute pressure at any two points, for the same tube of currents.
Beornoulli equation can be written as $$ P + \ rho gy + \ rho v ^ 2 = constant, $$ or, based on the figure, $$ P_1+\rho g y_1 +\rho (v_1)^2 =P_2+\rho g y_2 +\rho (v_2)^2,$$ where \(P\) is the pressure and the work-related term of the pressure applied in an area, \(\rho gy\) is the term for energy and potential of the fluid \(\rho (v)^2\), called the dynamic pressure, is the term connected to kinetic energy.Changes in fluid velocities are due to pressure differences. When the speed of a fluid increases, the pressure decreases and vice versa.
The velocity of the fluid will be given by $$ v_1 = \frac{A_2} {\sqrt{{A_1}^2-{A_2}^2}} \sqrt{2g \Delta H}, $$ where \(v_1\) is the velocity of the fluid in the non-strangulated section, \(A_1\) the cross-sectional area 1, \(A_2\) the cross-sectional area 2, \(g\) is the acceleration of gravity e \(\Delta H\) the difference in height.
Another Venturi meter model uses a U-tube, and is shown in the figure below.
In this case, the velocity of the fluid will be given by $$ v_1 = \frac{A_2} {\sqrt{{A_1}^2-{A_2}^2}} \sqrt{\frac{2 \color{goldenrod}{\rho_2} g \Delta h}{\color{blue}{\rho_1}}}, $$ \(v_1\) is the velocity of the density fluid \ (\ color {blue} {\ rho_1} \) in the section hho {\ color {blue} {\ rho_1} \(A_1\) the cross-sectional area 1, \(A_2\) the cross-sectional area 2, \(g\) is the acceleration of gravity and \(\Delta h\) the height difference of density yellow liquid (\ color {goldenrod} {\ rho_2} \).The viscosity is related to the friction between the molecules of a fluid, the greater the friction between the molecules the greater its viscosity. Honey under normal conditions is much more viscous than water. A fluid that has no viscosity is called an inverse. Zero viscosity is only observed at very low temperatures, in superfluids. Some fluids have such a high viscosity that they are considered solids, glass, tar, magma, etc.
Significance ratio = Inertial force / viscous force.
In most practical conditions, the flow in a circular tube is laminar to \(Re\) <2300, turbulent to \(Re\) > 4000 and transition between these values. Curiosity. In carefully controlled experiments, the laminar flow has been maintained for Reynolds numbers up to 100,000.
The table shows the viscosity (approximate) for some fluids.Viscosities | |
---|---|
Fluids | Viscosity (Pa.s) |
Helium (2K) | 0 |
Air (20 ° C) | 0,0000183 |
water (20 oC) | 0,00100 |
Olive oil (20 oC) | 0.084 |
Shampoo (20 oC) | 100 |
Honey (20 oC) | 1000 |
Common glass (540 oC) | 10¹³ |